Problem: Which of the following numbers is a multiple of 14? ${71,84,90,92,109}$
The multiples of $14$ are $14$ $28$ $42$ $56$ ..... In general, any number that leaves no remainder when divided by $14$ is considered a multiple of $14$ We can start by dividing each of our answer choices by $14$ $71 \div 14 = 5\text{ R }1$ $84 \div 14 = 6$ $90 \div 14 = 6\text{ R }6$ $92 \div 14 = 6\text{ R }8$ $109 \div 14 = 7\text{ R }11$ The only answer choice that leaves no remainder after the division is $84$ $ 6$ $14$ $84$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $84$ $84 = 2\times2\times3\times7 14 = 2\times7$ Therefore the only multiple of $14$ out of our choices is $84$. We can say that $84$ is divisible by $14$.